Section: Moadim   Category: Succos
Vilna Gaon: Why Is Succos On The 15th of Tishrei?

Chazal tell us that Succos should really be on Pesach because that is when we came out of Mitzrayim. The Vilna Gaon says however that the 15th day of Tishrei is really the appropriate time. Succos commemorates the Nes that Hashem surrounded us with the Ananei HaKavod and protected us in the harsh desert. When did we get the Ananei HaKavod? Originally, when we came out of Mitzrayim but after the Cheit HaEgel they went away. Only when Hashem forgave the Cheit HaEgel and we started to build the Mishkan did they come back. That of course happened on the 15th of Tishrei.

Here is the calculation according to the Gra. On Yom Kippur Moshe came down from 40 days in Shmayim with the second Luchos. The day after that he gathered Bnei Yisroel and commanded them to build the Mishkan. For the next two days they brought all the material they donated. The day after the materials were distributed to the workers and on the 15th they began to work.